A special quill exists which writes down the name of every magical child in Britain at the time of their birth, allowing Hogwarts letters to be sent to all magical children at the appropriate time, even those who are Muggle-born. The Hogwarts letter consists of a note of acceptance from the Deputy Headmaster or Headmistress of Hogwarts and a list of required textbooks and materials for the school year.
The letter is written on parchment paper and delivered to the recipient by owl, except in the case of Muggle-borns and magical children living with Muggles (such as Harry Potter), where the initial acceptance letter is delivered by the regular Muggle post. Hogwarts is able to magically tell whether or not a child has read his or her Hogwarts letter, as evidenced by the bombardment of 4 Privet Drive with letters, despite at least one of them having been opened and read by Vernon and Petunia Dursley.
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It is not possible to apply to Hogwarts, be it as a new student or a transfer. Students must reside in the United Kingdom- which encompasses England, Scotland, Ireland, Wales, and Northern Ireland.